Articles you may have missed...

I did, while I was out of town.

From the New York Times:  Forget What You Know About Good Study Habits

 But individual learning is another matter, and psychologists have discovered that some of the most hallowed advice on study habits is flat wrong. For instance, many study skills courses insist that students find a specific place, a study room or a quiet corner of the library, to take their work. The research finds just the opposite.

And from the Washington Post, a little opinion on:  School reform's meager results

Standard theories don't explain this meager progress. Too few teachers? Not really. From 1970 to 2008, the student population increased 8 percent and the number of teachers rose 61 percent. The student-teacher ratio has fallen sharply, from 27-to-1 in 1955 to 15-to-1 in 2007. Are teachers paid too little? Perhaps, but that's not obvious. In 2008, the average teacher earned $53,230; two full-time teachers married to each other and making average pay would belong in the richest 20 percent of households (2008 qualifying income: $100,240).

Enjoy.

Oxbridge

It is probably the most important day of your life. Your mind is racing and your hands are trembling at the thought of the erudite questions you are about to be asked, which will determine your future education, career and indeed the rest of your life. Then a man leans forward towards you and says: "Tell me about a banana."

other questions:

"Why isn't this chair acting as a wave?"(Chemistry, Oxford).

"Estimate the number of pebbles on Brighton Beach. If a pebble was given to each person would there be enough for the entire population?" (Natural sciences, Cambridge).

"If you leave the fridge turned on in a thermally isolated room, what happens to the room?" (Physics, Oxford).

Knowledge of a banana may be the key to Oxbridge entry
By Richard Garner
Monday, 6 September 2010

So You Want to Go to Oxbridge?: Tell Me About a Banana

Barry G on just-in-time learning

I think this is my favorite of Barry's articles -- he nails it.

Even worse than the book itself were the discussions in class that came out of it. One event in particular stands out. In a chapter that discussed the difference between "knowing" and "understanding," a chart presents examples of “Inauthentic versus Authentic Work.” In this chart “Practice decontextualized skills" is listed as inauthentic and "Interpret literature" as authentic. The black and white nature of the distinctions on the chart bothered me, so when the teacher asked if we had any comments, I said that calling certain practices “inauthentic” is not only pejorative but misleading. I asked the teacher “Do you really think that learning to read is an inauthentic skill?”

She replied that she didn’t really know about issues related to reading. Keeping it on the math level, I then referred to the chart's characterization of "Solve contrived problems" as inauthentic and “Solve ‘real world’ problems” as authentic and asked why the authors automatically assumed that a word problem that might be contrived didn’t involve “authentic” mathematical concepts. “Let’s move on,” she said.

[snip]

The authors’ approach to how one teaches for understanding is through a process that they call “backward design,” in which educators plan their courses, units and lessons by starting from what they want the end result to be. That is, what should students know, understand and be able to do? The planning process then entails working backwards from there, identifying the content that goes into this, the big ideas, the questions to be explored and so on.

As the authors state, backward planning is not a new idea. In fact, I was a bit confused as to why it is even needed, given that such work has essentially been done in the writing of the textbooks that cover the course material.... But this brings us to another axiom which I have heard repeated in education school, which states that textbooks are a resource and not a curriculum. The authors pick up on this as well and regard using the textbook for planning as a “sin," stating that “The textbook may very well provide an important resource but it should not constitute the syllabus.”

[snip]

In a paean to constructivism and the abandonment of textbooks, Tomlinson and McTighe dispose of the notion that sequence of topics and mastery of skills is important, calling such beliefs the “climbing the ladder” model of cognition. “Subscribers to this belief assume that students must learn the important facts before they can address the more abstract concepts of a subject,” the authors state, and then quote Lori Shepherd, a University of Colorado education professor to make their point:

“The notion that learning comes about by the accretion of little bits is outmoded learning theory. Current models of learning based on cognitive psychology contend that learners gain understanding when they construct their own knowledge and develop their own cognitive maps of the interconnections among facts and concepts.”

In fact, this is the crux of how they approach differentiated instruction. Sequence doesn’t matter. Each student constructs his or her own meaning at their own pace, by being immersed in what the authors term “contextualized grappling with ideas and processes.” What does this mean? There are many examples, but the prevalent pattern of instruction to emerge from the book seems to be one of giving students an assignment or problem which forces them to learn what they need to know in order to complete the task. Say it is quadratic equations. Rather than teach them the various methods of factoring first, with the attendant drills, they might start with a problem such as x^2 + 5x + 6 = 0. The teacher may then provide some activities that illustrate what factoring is, and then provide some exercises. The goal would be to factor the above equation into (x+3)(x+2) = 0 and, from there, lead the students to see that there are two values that satisfy the equation. This is what they mean by “contextualized grappling” as opposed to “decontextualized drill and practice.” It is a “just in time” approach to learning, (my choice of phrase, not theirs) in which the tools that students need to master are dictated by the problem itself by not burdening the student's mental inventory with “mind numbing” drills for mastery of a concept or skill until it is actually needed.

[snip]

They admit that there are times when direct instruction or ‘teaching by telling’ might work extremely well. “There is a need for balance between student construction of meaning and teacher guidance”, they proclaim. That direct instruction would work even better if topics were presented in a logical sequence is not the message of this particular book, however.

[snip]

“Just in time” approaches that work as a model for business inventory work just as well in education, they believe. The result is an approach that is like teaching someone to swim by throwing them in the deep end of a pool and telling them to swim to the other side. For the students who may already know a bit about swimming, they may choose to take that opportunity to learn the butterfly. The teacher might advise the weaker students to learn the breast stroke and provide the much needed direct instruction which they may now choose to learn. Or not.

Let’s move on.

rule of 20

Surprisingly, the vast majority of skills which we try to teach appear to begin the passage from acquisition to fluency-building at roughly the same point —when correct frequencies are somewhere between 14 and 20 per minute, and an accuracy of between 67% and 83% has been achieved. That rule seems to apply to very basic behaviors like pointing to named objects, steps taken while walking, and completing parts of a dressing sequence. The same transition point also seems to apply to very complex behaviors like reading, speaking, and writing digits to solve advanced mathematics problems. Indeed, the rule appears so universal that when Sokolove (note 9) examined circa 3300 programs of children in grades 1 through 6, the “rule of 20” predicted progress in more than 97% of the cases.

Decisions, Decisions
Owen Roberts White
University of Washington
Fall 2000

unfriendly worksheets, part 2

from A Guide to Learning English:

Rule number 2: Be aware of the difficulties of cultural references!

The following text is the first part of the introductory paragraph to a question about car speed:

"The police used to measure the speed of cars on the road by having two PCs some distance apart using a stopwatch. One of them would stand and wave as a car reached him. When the wave was seen by the second PC a stopwatch was started. As the car passed the second PC, the stopwatch was stopped."

The question itself read:

"Is the car exceeding the maximum speed limit in Britain?"

The ESL student who asked for my help with this question was puzzled how a personal computer could stand and wave. He also had no idea what the maximum speed limit is in Britain.

I would like to know how two personal computers can stand some distance apart and use a stopwatch.

unfriendly worksheets

source:
A Guide to Learning English

Pass/Fail

Examination dreams are reported to persist even into old age...
- Time magazine

You will never graduatefrom this dream
of blue books.
No matter how
you succeed awake,
asleep there is a test
waitinmg to be failed.
The dream beckons
with two dull pencils,
but you haven't even taken the course;
when you reach for a book--
it closes its door
in your face; when
you conjugate a verb--
it is in the wrong
language
Now the pillow becomes
a blank page. Turn it
to the cool side;
you will still smother
in all of the feathers
that have to be learned
by heart.

Linda Pastan
1975

in:
The Compact Bedford Introduction to Literature
Michael Meyer

edu-fads at home

Found this comment on Jay Mathews' 2009 column about 21st century skills:

One of my friends holds advanced degrees in education, and she used cutting-edge methods to teach her own kids. What she forgot was the classic problem of the teacher being all fired up and motivated, and the student feeling left out of the picture. After all, fundamentals may be old-hat for teachers, but for students they're all new concepts. Her son was all but forgotten in her enthusiasm and fascination with the perpetually new. She has asked me a hundred times what I think is "wrong" with him (answer: "you").

She force-fed her son this and that fad over the years while he quietly turned off to learning. He recently dropped out of the marginal college he was able to squeak into with his middling test scores, yet it is obvious to anyone who talks with him for five minutes that he is very bright. I think he'll probably drop back in some day when he returns for his own reasons, but his mom's incessant buzz-speak about the latest pedagogical gewgaws of the day (I suspect 21st-century skills were part of it) really did a number on him. Poor kid.
1/5/2009 7:10:48

The Latest Doomed Pedagogical Fad: 21st-Century Skills
by Jay Mathews
Washington Post
Monday, January 5, 2009

I wonder if this boy was being homeschooled or afterschooled.

survey: charter support at 65%

Support for charter schools also continued to grow among the public, with 65 percent of respondents saying they would back new public charter schools in their community and 60 percent saying they would support “a large increase” in the number of such schools operating in the United States.

Fewer Americans Back Obama’s Education Programs
By Dakarai I. Aarons
Published Online: August 25, 2010

I'm glad to see this level of support for charters, but I do worry about charters killing off private and parochial schools.

Robert Pondiscio on curriculum vs value-added

When I think of the curriculum and teaching methods I was required to use in my classroom, the idea that my effectiveness might be dependent upon them makes me want to lie down with a damp wash cloth on my forehead. Manipulatives and discovery instead of basic arithmetic? Endlessly revising ”small moments” and teaching the writing process to 10-year olds instead of basic grammar? No time for even basic science, social studies because of district demands for ever larger math and literacy blocks? If it fails, it’s on me? Seriously?

Erin Johnson left a comment:

Robert, Why do you think that the LA Teachers Union (or the national unions) have not highlighted the issue of curricula?

I have recently been in contact with a LA teacher who was rated “more effective” in math by the LA Times. She states that her good rating was probably due to the fact that she “subversively” uses Saxon math instead of her district adopted program. Do ed reformers expect that teachers will subvert the curricula adoption process?

And here is Robert again:

I’m not sure curriculum reform is on anyone’s radar screen in a big way, including the unions. I used to regularly subvert…er…adapt my math curriculum to assure automaticity on basic functions. 5th graders counting on their fingers or multiplying with arrays is an offense to my sensibilities. I had less flexibility on ELA since there was lots of joint planning and execution involved. I’d go as far as saying my school’s ELA program (“It’s not a curriculum, Mr. Pondiscio, it’s a philosophy,” I can still hear the staff developer reminding me) is what turned me into a curriculum advocate.

Curriculum effects and value-added

cart, horse

from Casting Out Nines:

[I]t’s not clear to me that doing “algebra” is a better idea here than just doing straight-up subtraction.  What’s to be gained by saying “the whole is 8; one part is 3; the other part is ____” versus “What is 8 minus 3?” Again, maybe I’m out of touch, but subtraction is a fundamental skill that algebra builds upon; doing algebra before subtraction seems a little backwards to say the least. A kid who is comfortable with subtraction will be able to do these whole/part problems in a snap by using subtraction. A kid doing these “algebra” problems basically has to invent subtraction in order to do them, or else draw pictures of balloons and start counting. It feels like the curriculum is trying to be intentionally nontraditional here, just for the sake of doing things differently rather than because it works better.

what makes this question difficult?

This is one of the lowest percent corrects I've seen on a Question of the Day -- as low as the percent correct for the 3 people in an office question.

Why is that?

Critique of Envision Math by Casting Out Nines (Robert Talbert)

From January, 2008:

Four questions about this:

1. Should it be a requirement of parenthood that you must remember enough 5th grade math to teach it halfway decently to your kids?
2. Does the smartboard come included with the textbooks?
3. Did anybody else have the overwhelming urge to yell “Bingo!” after about 2 minutes in?
4. When will textbook companies stop drawing the conclusion that because kids today like to play video games, talk on cell phones, and listen to MP3 players, that they are therefore learning in a fundamentally different way than anybody else in history?

The last question is all about the research-free digital nativist assumption that is the source of many lucrative curriculum deals these days. Data, please?

I've added emphasis

basically laughing it off the blogosphere for its happy-clappy, uncritical acceptance of unproven digital nativist frameworks and for going way over the top with smartboards. Little did I know that my own offspring would be in the middle of it just three years later. So, in an effort to process what she’s doing (for me, for her, and for anybody else who cares), this is the first of what might be many posts about the specifics of enVisionMATH, as viewed by a parent whose kid happens to be learning from that curriculum, and who also happens to be a mathematician and math teacher.

So I suggest you bookmark Casting Out Nines and see what develops.

Steve H on setting up problems

re: how many unknowns?

I like to use more variables than are needed because I find it easier to create correct equations. I know that I can always turn the algebra crank later without much thought.

r+s=12 is easy and I know that it's correct. I also know that the half perimeters are pi*r and pi*s.

I then look for enough equations to meet my unknowns. That is what's funny about this problem. You don't have enough information to directly solve for the answer before you look at the choices. There are not enough equations for the variables. Even if you use just r and (12-r), you have no equation, unless, that is, you plug in each answer.

I don't like problems like this, because my first reaction is that you don't have enough information. You do, however, if you look at the possible answers.

Also, why is there no variable in the answer? It's just a unique aspect of this particular problem. What if one of the semicircles is replaced by half of a square? You would have something like this:

4r + (12-r)*pi

for the perimeter. the variable does not disappear when the expression is reduced.

You can't trust what you think because problems try very hard to trick your understanding. You just have to follow the facts (equations) and see where they lead you. As I always say, let the math give you the understanding, not the other way around.

how many unknowns, part 2

gasstationwithoutpumps said:

Although Glen would never create 2 unknowns, preferring r and 12-r to r and s, I often find it easier to create multiple unknowns when initially setting up the problem, then remove the unnecessary ones. In this case, it was easier to remove (r+s) as a single unit, and never worry about manipulating 12-r.

I can't tell you all how important these threads have been to me: how much I'm learning (I hope I'm learning - !) and how rich the experience has been.

It's led me to think about the question of self-teaching a bit. Until last night, I had simply never thought about 'how many unknowns' in the way you all are talking about unknowns now. I had never thought about it because, where unknowns are concerned, the books seem to suggest that less is more.

Mind you, I don't think any math book I've used has directly stated that 12 - r is superior to r + s=12. I'm pretty sure I inferred that it was based in the fact that I don't recall any instances of r + 12 where 12 - r was a possibility.

This strikes me as the kind of thing a good math teacher would bring up in class, perhaps as an aside?

Or something that would come up in discussion?

What do you think?

poll: top education books of the decade

at Education Next

hmmmm...

Teach Like a Champion isn't on the list.

I find that incredible. 

Not sure I'll vote.

how many unknowns?

re: how many unknowns in the two half-circle problem, Glen wrote:

I would never create two unknowns in a situation like this, where the two radii are not independent. Since the distance from R to S was given as 12, the radius of one circle made a good unknown, and the radius of the other was 12 minus that SAME unknown. Either circle would do, of course.

The length of the curve can then be expressed in terms of the one unknown for both semicircles. Using the left circle, and calling its radius r, the right has to be 12-r, so the two semicircles added together were,

= pi*r + pi(12-r)
= pi*r + pi*12 - pi*r
= 12pi

If I took part of my $100 and gave it to a friend, there would be only one unknown. Whether you made it the amount I gave him, or the amount that I kept, or the percent I gave him, or the percent I kept, or the difference in dollars or percent or fraction between what he got and what I kept, or the ratio of our money, or whatever, there is only one unknown. Everything else in such a problem can be expressed in terms of that one unknown, which usually makes the problem easier to manage.

THIS is what I was trying to do.

THIS is what I always do, if possible.

I don't know what the problem was.

Inflexible knowledge?

Heat prostration?

I'm half serious about the heat. I took the test outside in 85+ temp. All summer long I've had severe performance deterioration any time I work in the heat. One day, when the temperature was close to 100, I found myself unable to solve even the simplest of problems. I sat at the picnic table working the same problems over and over again in slow motion. Five, 6, 7 times. Or more. I'd crawl through the problem, check my (wrong) answer, then go back to the beginning and crawl through it again and then again until finally the correct answer appeared.

Then I'd go on to the next problem and do that one 6 or 7 times.

I love summer. Have to soak up the sun while I can.

Big Calendar pin-up

fair warning

If all goes as planned, I am going to begin working through the Unit 5 worksheets from the Arlington Algebra Project, as lgm suggested. Tonight.

I say 'fair warning' because there's no answer key.

order of operations

I mentioned Martha Kolln's Rhetorical Grammar in a comment on "math writing."

Martha Kolln is part of my Great Unread, unfortunately. Along with Polya.

So, since I don't know enough about rhetorical grammar (pdf file) to write a post about it, here is a terrific passage from Geoffrey Pullum's 50-year anniversary take-down of Strunk and White, which I believe is the kind of analysis Kolln does:

"Use the active voice" is a typical section head. And the section in question opens with an attempt to discredit passive clauses that is either grammatically misguided or disingenuous.

We are told that the active clause "I will always remember my first trip to Boston" sounds much better than the corresponding passive "My first visit to Boston will always be remembered by me." It sure does. But that's because a passive is always a stylistic train wreck when the subject refers to something newer and less established in the discourse than the agent (the noun phrase that follows "by").

For me to report that I paid my bill by saying "The bill was paid by me," with no stress on "me," would sound inane. (I'm the utterer, and the utterer always counts as familiar and well established in the discourse.) But that is no argument against passives generally. "The bill was paid by an anonymous benefactor" sounds perfectly natural. Strunk and White are denigrating the passive by presenting an invented example of it deliberately designed to sound inept.

April 17, 2009
50 Years of Stupid Grammar Advice
By Geoffrey K. Pullum

thanks to Karen H